lim x → 0 √x^2+100 - 10/x^2 will be?
- Does not exist
- 1/20
- ∞
- None of these
Explanation
To evaluate the limit:
lim (x→0) (√(x^2+100) - 10)/x^2
Rationalize the numerator:
= lim (x→0) ((x^2+100) - 100) / (x^2(√(x^2+100) + 10))
= lim (x→0) x^2 / (x^2(√(x^2+100) + 10))
Cancel x^2:
= lim (x→0) 1 / (√(x^2+100) + 10)
As x→0, √(x^2+100) → √100 = 10:
= 1 / (10 + 10)
= 1 / 20
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